notes from Gilad Brachas talk wrt functor, monad, semigroup, monoid.The observation that a monoid is foldRightable is interesting.

gistfile1.txt

a semigroup is addable

a monoid is foldRightable or aggregatable
(ie addable, zero)

a functor is mappable
 
a monad is chainable or flatmappable

strong suit of monads:
pipelining using a for comprehension, handle different outcomes, null, deferred outcomes until the first future completes etc
Erik Meijer calls this: focus on the happy path

a ring is multipliable 
in addition to addable and additive zero
 
Kleisli arrows are a way of composing functions that return options etc without having to do a for comprehension

the monad contract:
new C(x).flatMap(f) == f(x);
c.flatMap((x)=> new C(x)) == c;
c.flatMap((x)=> f(x).flatMap(g)) ==
c.flatMap(f).flatMap(g);